Nor should "Men's Day", or any kind of "Day" celebration dedicated to a group of people based on their gender, race, sexual orientation, or any such inconsequential characteristics.
Consider this description that, for example, Facebook gives of Women's Day: "Let's celebrate the amazing contributions women make to our world and our future."
"Women" is taken as a homogeneous group, and contributions made by some of them are attributed to all of them. Like they were some kind of hive mind that acts in unison.
This is such a collectivist way of thinking. As a devout individualist, this kind of thinking clashes badly with my principles.
As an individualist, I strongly endorse the rights of the individual, as well as treating and judging people based on their personal merits, qualifications, achievements, actions, personality and content of character, regardless of what their gender, race or sexual orientation may be.
If an individual person has made a significant contribution to society and humanity, that may well be worthy of appreciation and respect. However, taking a physical inconsequential characteristic of said person, and using that to give credit for that contribution to all people who happen to share that same characteristic, is abhorrent.
If there is a woman who has made a great contribution to society and humanity, I'm all for recognizing and celebrating that. But not because she is a woman, but because she is a person who has made such a contribution. It doesn't really matter whether she is a woman, a man, or anything else. What matters what she has done, not what she is.
Special treatment (usually special services) should only be granted to groups of people if there is a scientifically provable medical or biological reason for it, for practical and pragmatic reasons, but that's about it. Other than physical necessity, people should always be treated as individuals, based on their personal merits, not based on what they are.